## In Search of a Good Map Projection, by Lance Nelson

#### (Notes for a class discussion on choosing a map projection by Lance Nelson. kam

The first step in chosing a projection is to determine:

• Location
• Size
• Shape

These three things determine where the area to be mapped falls in relation to the distortion pattern of any projection. One "traditional" rule described by Maling (Maling, 1992) says:

• A country in the tropics asks for a cylindrical projection.
• A country in the temperate zone asks for a conical projection.
• A polar area asks for an azimuthal projection.

Implicit in these rules of thumb is the fact that these global zones map into the areas in each projection where distortion is lowest:

• Cylindricals are true at the equator and distortion increases toward the poles.
• Conics are true along some parallel somewhere between the equator and a pole and distortion increases away from this standard.
• Azimuthals are true only at their center point, but generally distortion is worst at the edge of the map.

If every place we wanted to map lined up nicely into these areas of minimal distortion we would be home-free, jumping to the next step of choosing "special properties". A little experience shows that geographic space is not so fine and regular and many places will always fall outside the good areas on the basic projections. One easy way to adjust for this is to change the aspect of the projection. This translates the distortion pattern in the projection space so the areas of least distortion are moved to another geographic area. Even with this added flexibility the choices are sill pretty limiting. Malling suggests that various modifications are possible to make a projection work better:

• Redistribution of scales and using more than one line of zero distortion, such as in a secant case.
• Imposition of special boundary conditions.
• Using the projection more than once to get recentred or interrrupted maps.
• Combining projections. (Mechanically or mathematically)

Although we may have succeeded in minimizing distortion in general, we still need to consider the special properties of a projection. For a particular map-use the map may need to be conformal, equal area, or some compromise of these. In some cases, such as navigation, conformality is absolutely necessary. In statistical mapping, equivalence is necessary.

The final projection choice would seem to be a fairly straightforward function of minimized distortion and special properties. In the end though, there are several other factors that will influence choices.

Sometimes it is not necessary to consider special properties. At large scales the differences introduced by distortion cannot be measured on many maps.

Maling notes that there is a perceptual threshold of about 0.2mm for human map users and so there is some information that a human user cannot extract from a printed map. On the other hand, digital data might contain more information than a computer should extract. This may present problems in comparing data, that in human terms, is the same.

Maling, D.H. 1992. Coordinate Systems and Map Projections, 2nd Ed. Pergamon Press. Oxford.